基于增益调度的防空导弹控制系统设计
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摘要
拦截导弹通过精确制导实现与机动目标直接碰撞,利用动能将目标彻底摧毁。在距离地面约20km高度,拦截导弹的气动外形可以保证精确制导所需要的机动能力,但是响应速度却因为舵控效率的减弱而大大降低,采用直接侧向力与气动力的复合控制方式则可以显著提高拦截导弹控制系统的响应速度。本文基于增益调度方法对复合控制律进行了设计。
首先对带有侧向喷流装置的拦截弹的数学模型进行了推导,然后在工作点对模型进行了线性化,从而建立了导弹的线性变参数模型。并以俯仰方向为例,设计了导弹直接侧向力与气动力复合控制系统。
针对由脉冲发动机提供直接侧向力的拦截导弹,本文采用了这样的设计思路,即先独立设计舵控制律,然后把设计好舵控制律的系统整合成新受控对象,与离散控制量——脉冲发动机点火数量构成新控制系统。并将动态增益调度方法应用于过载指令跟踪控制系统设计。通过与静态增益调度方法和固定系数方法进行比较,得出动态增益调度方法能够更好的跟踪过载指令,而且改善了舵系统的响应。
因为脉冲发动机的数量有限,为了节省脉冲发动机,本文给出了拦截导弹稳定跟踪上过载指令后,直接侧向力不输出的条件以及数学证明。并且通过仿真,验证该条件的正确性。
最后,综合拦截导弹运动模型和目标机动模型,对飞机和再入大气层的弹道导弹目标完成了从中制导段到遭遇的拦截过程仿真。给出了拦截导弹和目标的相对运动曲线和脱靶量的Monte-Carlo仿真结果。仿真结果表明,拦截导弹能够很好的完成拦截飞机和弹道导弹任务。
A hit-to-kill interceptor achieves direct collision with a maneuverable target by precision guidance, and destroys the target with kinetic energy. At about 20km altitude, the aerodynamic shape of the interceptor is able to create a desired divert acceleration for precision guidance, but the response to a guidance command is getting much slower because of the control fin’s weak effectiveness. The blended control, which means the combination of lateral thrust control and aerodynamic control, can evidently increase the response speed of the interceptor’s control system. In this thesis, the design of aerodynamic and lateral thrust blended control law using the gain scheduling method is investigated.
First of all, the nonlinear model of interceptor with lateral thrust is deduced. Then the plant is linearized around different operating points, and which leads to the linear parameter-varying model. With the pitch loop as an example, we design the missile’s lateral thrust and aerodynamics blended control system.
Assuming that the lateral thrust is provided by impulse thrusters, we design the control system with the following strategy. The tail fin’s controller is designed independently, and then all the continuous parts, including the fin’s controller, are reunited into a new controlled plant of the ignition number of the impulse thrusters which is in discrete-time form. A dynamic gain scheduling method is employed in the system design. Compared with the static gain scheduling and fixed gain method, the dynamic gain scheduling gives better transient performance and improves the transient performance of tail fins.
The problem about how to save the impulse thrusters is discussed. Theoretically, we give the possibility of decreasing the use of impulse thrusters. Then we use simulation to verify the idea.
Finally, we simulate the interception processes against an airplane or a reentry ballistic missile target from the mid-course guidance to the engagement. The simulation results prove that the interceptor can hit the target effectively.
首先对带有侧向喷流装置的拦截弹的数学模型进行了推导,然后在工作点对模型进行了线性化,从而建立了导弹的线性变参数模型。并以俯仰方向为例,设计了导弹直接侧向力与气动力复合控制系统。
针对由脉冲发动机提供直接侧向力的拦截导弹,本文采用了这样的设计思路,即先独立设计舵控制律,然后把设计好舵控制律的系统整合成新受控对象,与离散控制量——脉冲发动机点火数量构成新控制系统。并将动态增益调度方法应用于过载指令跟踪控制系统设计。通过与静态增益调度方法和固定系数方法进行比较,得出动态增益调度方法能够更好的跟踪过载指令,而且改善了舵系统的响应。
因为脉冲发动机的数量有限,为了节省脉冲发动机,本文给出了拦截导弹稳定跟踪上过载指令后,直接侧向力不输出的条件以及数学证明。并且通过仿真,验证该条件的正确性。
最后,综合拦截导弹运动模型和目标机动模型,对飞机和再入大气层的弹道导弹目标完成了从中制导段到遭遇的拦截过程仿真。给出了拦截导弹和目标的相对运动曲线和脱靶量的Monte-Carlo仿真结果。仿真结果表明,拦截导弹能够很好的完成拦截飞机和弹道导弹任务。
A hit-to-kill interceptor achieves direct collision with a maneuverable target by precision guidance, and destroys the target with kinetic energy. At about 20km altitude, the aerodynamic shape of the interceptor is able to create a desired divert acceleration for precision guidance, but the response to a guidance command is getting much slower because of the control fin’s weak effectiveness. The blended control, which means the combination of lateral thrust control and aerodynamic control, can evidently increase the response speed of the interceptor’s control system. In this thesis, the design of aerodynamic and lateral thrust blended control law using the gain scheduling method is investigated.
First of all, the nonlinear model of interceptor with lateral thrust is deduced. Then the plant is linearized around different operating points, and which leads to the linear parameter-varying model. With the pitch loop as an example, we design the missile’s lateral thrust and aerodynamics blended control system.
Assuming that the lateral thrust is provided by impulse thrusters, we design the control system with the following strategy. The tail fin’s controller is designed independently, and then all the continuous parts, including the fin’s controller, are reunited into a new controlled plant of the ignition number of the impulse thrusters which is in discrete-time form. A dynamic gain scheduling method is employed in the system design. Compared with the static gain scheduling and fixed gain method, the dynamic gain scheduling gives better transient performance and improves the transient performance of tail fins.
The problem about how to save the impulse thrusters is discussed. Theoretically, we give the possibility of decreasing the use of impulse thrusters. Then we use simulation to verify the idea.
Finally, we simulate the interception processes against an airplane or a reentry ballistic missile target from the mid-course guidance to the engagement. The simulation results prove that the interceptor can hit the target effectively.
引文
1穆利军,蔡远文.国外战略导弹的现状及发展趋势.兵工自动化. 2007, 26(4):L03-L07
2 S. W. Thurman. Robust Digital Autopilot Design for Spacecraft Equipped with pulse-operated Thrusters. Journal of Guidance, Control and Dynamics. 1996, 19(5):1047-1055
3万自明.防空防天导弹精确控制技术及其研究需求综述.现代防御技术. 2004, 32(2):36-41
4 W. R. Chadwick. Augmentation of High-Altitude Maneuver Performance of a Tail-Controlled Missile Using Lateral Thrust. AD-A328973
5 W. R. Chadwick and P. Zarchan. Interception of Spiraling Ballistic Missiles. Proceedings of the American Control Conference, Seattle, Washington, 1995:4476-4483
6 J. I. Lee, I. J. Ha. Autopilot Design for Highly Maneuvering STT Missiles via Singular Perturbation-Like Technique. IEEE Transactions on Control Systems Technology. 1999, 7(5):527-541
7张友安,杨华东,顾文锦.空空导弹控制系统一体化设计方法研究.现代防御技术. 2003, 31(4):17-20
8李聪颖,顾文锦,王士星.飞航导弹增益调度AWCT PID自动控制系统设计.战术导弹控制技术. 2004, (2):8-12
9 A. Spencer and W. Moore. Design Trade-offs for Homing Missiles. AIAA-1992-2755
10 B. Y. Min, J. W. Lee and Y. H. Byun. Numerical Investigation of the Shock Interaction Effect on the Lateral Jet Controlled Missile. Aerospace Science and Technology. 2006, 10:385-393
11 A. Spencer. Optimal Control Thruster Location for End Atmospheric Interceptors. AIAA-1993-2639
12 R. D. Weil and K. A. Wise. Blended Aero & Reaction Jet Missile Autopilot Design Using VSS Techniques. Proceedings of the 30th Conference on Decision and Control, Brighton, English, 1991:2828-2829
13 M. Innocenti and A. Thukral. Simultaneous Reaction Jet and AerodynamicControl of Missile Systems. AIAA-1993-3739
14 M. Innocenti and A. Thukral. Robustness of Variable Structure Control System for Maneuverable Flight Vehicles. Journal of Guidance, Control and Dynamics. 1997, 20(2):377-383
15 A. Thukral and M. Innocenti. Variable Structure Autopilot for High Angle of Attack Maneuvers Using On-off Thrusters. Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, 1994:3850-3851
16 A. Thukral and M. Innocenti. A Sliding Mode Missile Pitch Autopilot Synthesis for High Angle of Attack Maneuvering, IEEE Transactions on Control System Technology. 1998, 6(3):359-371
17程凤舟,万自明,陈士橹,于本水.防空导弹直接力与气动力复合控制系统设计.飞行力学. 2003, 21(2):49-52
18郑逸峰,姜长生.拦截导弹直接力与气动力复合控制问题研究.弹箭与制导学报. 2005, 25(4):484-487
19万自明,李玉林,黄荣度.空气动力和直接侧向力复合控制的拦截弹飞行力学及稳定回路模型.现代防御技术. 2003, 31(2):18-22, 28
20李玉林,刘庆鸿.直接力/气动力复合控制拦截弹的飞行控制系统设计.弹箭与制导学报. 2006, 26(4):7-10
21 D. B. Ridgely, Y. Lee and T. Fanciullo. Dual Aero/Propulsive Missile Control-Optimal Control and Control Allocation. AIAA-2006-6570
22 D. B. Ridge, D. Drake, L. Triplett and C. Geise. Dynamic Control Allocation of a Missile with Tails and Reaction Jets. AIAA-2007-6671
23 C. Tournes, Y. Shtessel and I. Shkolnikov. Missile Controlled by Lift and Divert Thrusters Using Nonlinear Dynamic Sliding Manifolds. Journal of Guidance, Control and Dynamics. 2006, 29(3):617-625
24 P. K. Menon and V. R. Iragavarapu. Adaptive Techniques for Multiple Actuator Blending. AIAA-1998-4494
25邹晖,陈万春,王鹏,殷兴良.敏捷导弹气动力/侧向推力复合控制特性分析研究.北京航空航天大学学报. 2004, 30(3):192-196
26周锐,王军.导弹气动力/直接力自适应控制分配及优化设计.航空学报. 2007, 28(1):187-190
27 R. Hirokawa, K. Sato and S. Manabe. Autopilot Design for a Missile with Reaction-Jet Using Coefficient Diagram Method. AIAA-2001-4162
28李友年,贾晓洪.一种敏捷导弹控制系统的设计方法.航空兵器. 2005, 4:13-15
29贾晓洪,凡永华,杨军.一种气动力/直接力复合控制导弹自动驾驶仪设计.弹箭与制导学报. 2005, 25(3):1-3
30贾晓洪,凡永华,杨军.气动力/直接力复合控制导弹自动驾驶仪的鲁棒稳定性分析.弹箭与制导学报. 2005, 25(4):1-2
31王鹏,陈万春,殷兴良.空空导弹大角度姿态反作用喷气控制.航空学报. 2005, 26(3):263-267
32沈明辉,陈磊,吴瑞林,周伯昭.大气层内动能拦截弹的变增益鲁棒姿控系统设计研究.宇航学报. 2007, 28(3):562-565
33王宇航,马克茂.直接力与气动力复合控制系统姿态稳定问题研究.宇航学报. 2007, 28(4):840-844
34宋明军,魏明英,李君龙.某高制导精度拦截器稳定控制系统设计方法比较研究.现代防御技术. 2003, 31(3):37-40
35魏明英,宋明军.拦截器姿态控制系统切换控制方法研究.系统工程与电子技术. 2007, 29(1):118-120
36周荻,邵春涛.大气层内拦截弹直接侧向力/气动力混合控制系统设计.宇航学报. 2007, 28(5):1205-1209
37 H. K. Khalil. Nonlinear Systems. Third Edition. Publishing House of Electronics Industry, 2007:485-499
38 J. M. Biannic, P. Apkarian. Missile Autopilot Design via a Modified LPV Synthesis Technique. Aerospace Science and Technology. 1999, 3:153-160
39 W. J. Rugh, J. S. Shamma. Research on Gain Scheduling. Automatica. 2000, 36(10):1401-1425
40李中健,安锦文.全包线飞行控制系统设计方法研究.飞行力学. 2001, 19(1):5-8
41 R. W. Howard. Automatic Flight Controls in Fixed Wing Aircraft: The First 100 years. Aeronautical Journal. 77, 533-562
42 J. S. Shamma, J. R. Cloutier. Trajectory Scheduled Missile Autopilot Design. Proceedings of the 1st IEEE Conference on Control Applications, Dayton, OH. 1992:237-242
43 N. Sureshbabu, W. J. Rugh. Output Regulation with Derivative Information. IEEE Transactions on Automatic Control. 1995, 40(10):1755-1766
44 H. Tan, W. J. Rugh. Nonlinear Overtaking Optimal Control: Sufficiency, Stability and Approximation. IEEE Transactions on Automatic Control. 1998, 43(12):1703-1718
45 A. Leonessa, W. M. Haddad, V. Chellaboina. Nonlinear System Stabilization via Stability-based Switching. Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL. 1988:2983-2996
46 M. W. McConley, B. D. Appleby, M. A. Dahleh. Control Lyapunov Function Approach to Robust Stabilization of Nonlinear Systems. Proceedings of the American Control Conference, Albuquerque, NM. 1997:416-419
47 J. R. Cloutier, C. N. D’Souza, C. P. Mracek. Nonlinear Regulation and Nonlinear H-infinity Control via the State-dependent Riccati Equation Technique. Proceedings of the 1st International Conference on Nonlinear Problems in Aviation and Aerospace, Daytona, FL. 1996:117-130
48 T. S. Richardson, P. M. Davison, M. H. Lowenberg and M. di Bernardo. Control of Nonlinear Aircraft Models Using Dynamic State-Feedback Gain Scheduling. AIAA-2003-5503
49 C. D. C. Jones, M. H. Lowenberg and T. S. Richardson. Tailored Dynamic Gain-Scheduled Control. Journal of Guidance, Control and Dynamics. 2006, 29(6):1271-1281
50 M. N. Hammoudi, M. H. Lowenberg. Dynamic Gain Scheduled Control of an F16 Model. AIAA-2008-6487
51 E. Devaud, H. Siguerdidjane and S. Font. Nonlinear Dynamic Autopilot Design for the Non-minimum Phase Missile. Proceedings of the 37th IEEE Conference on Decision & Control. 1998:4691-4696
52 J. I. Lee and I. J. Ha. Autopilot Design for Highly Maneuvering STT Missiles via Singular Perturbation-Like Technique. IEEE Transactions on Control Systems Technology. 1999, 7(5):527-541
53 J. Hauser, S. Sastry and G. Meyer. Nonlinear Control Design for Slightly Non-minimum Phase Systems: Application to V/STOL Aircraft. Automatica. 1992, 28(4):665-679
54钱杏芳,林瑞雄,赵亚男.导弹飞行力学.北京理工大学出版社.北京, 2000:23-25, 28-48
55 P. Zarchan. Tactical and Strategic Missile Guidance. Second Edition. AIAA,1994:25-30
2 S. W. Thurman. Robust Digital Autopilot Design for Spacecraft Equipped with pulse-operated Thrusters. Journal of Guidance, Control and Dynamics. 1996, 19(5):1047-1055
3万自明.防空防天导弹精确控制技术及其研究需求综述.现代防御技术. 2004, 32(2):36-41
4 W. R. Chadwick. Augmentation of High-Altitude Maneuver Performance of a Tail-Controlled Missile Using Lateral Thrust. AD-A328973
5 W. R. Chadwick and P. Zarchan. Interception of Spiraling Ballistic Missiles. Proceedings of the American Control Conference, Seattle, Washington, 1995:4476-4483
6 J. I. Lee, I. J. Ha. Autopilot Design for Highly Maneuvering STT Missiles via Singular Perturbation-Like Technique. IEEE Transactions on Control Systems Technology. 1999, 7(5):527-541
7张友安,杨华东,顾文锦.空空导弹控制系统一体化设计方法研究.现代防御技术. 2003, 31(4):17-20
8李聪颖,顾文锦,王士星.飞航导弹增益调度AWCT PID自动控制系统设计.战术导弹控制技术. 2004, (2):8-12
9 A. Spencer and W. Moore. Design Trade-offs for Homing Missiles. AIAA-1992-2755
10 B. Y. Min, J. W. Lee and Y. H. Byun. Numerical Investigation of the Shock Interaction Effect on the Lateral Jet Controlled Missile. Aerospace Science and Technology. 2006, 10:385-393
11 A. Spencer. Optimal Control Thruster Location for End Atmospheric Interceptors. AIAA-1993-2639
12 R. D. Weil and K. A. Wise. Blended Aero & Reaction Jet Missile Autopilot Design Using VSS Techniques. Proceedings of the 30th Conference on Decision and Control, Brighton, English, 1991:2828-2829
13 M. Innocenti and A. Thukral. Simultaneous Reaction Jet and AerodynamicControl of Missile Systems. AIAA-1993-3739
14 M. Innocenti and A. Thukral. Robustness of Variable Structure Control System for Maneuverable Flight Vehicles. Journal of Guidance, Control and Dynamics. 1997, 20(2):377-383
15 A. Thukral and M. Innocenti. Variable Structure Autopilot for High Angle of Attack Maneuvers Using On-off Thrusters. Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, 1994:3850-3851
16 A. Thukral and M. Innocenti. A Sliding Mode Missile Pitch Autopilot Synthesis for High Angle of Attack Maneuvering, IEEE Transactions on Control System Technology. 1998, 6(3):359-371
17程凤舟,万自明,陈士橹,于本水.防空导弹直接力与气动力复合控制系统设计.飞行力学. 2003, 21(2):49-52
18郑逸峰,姜长生.拦截导弹直接力与气动力复合控制问题研究.弹箭与制导学报. 2005, 25(4):484-487
19万自明,李玉林,黄荣度.空气动力和直接侧向力复合控制的拦截弹飞行力学及稳定回路模型.现代防御技术. 2003, 31(2):18-22, 28
20李玉林,刘庆鸿.直接力/气动力复合控制拦截弹的飞行控制系统设计.弹箭与制导学报. 2006, 26(4):7-10
21 D. B. Ridgely, Y. Lee and T. Fanciullo. Dual Aero/Propulsive Missile Control-Optimal Control and Control Allocation. AIAA-2006-6570
22 D. B. Ridge, D. Drake, L. Triplett and C. Geise. Dynamic Control Allocation of a Missile with Tails and Reaction Jets. AIAA-2007-6671
23 C. Tournes, Y. Shtessel and I. Shkolnikov. Missile Controlled by Lift and Divert Thrusters Using Nonlinear Dynamic Sliding Manifolds. Journal of Guidance, Control and Dynamics. 2006, 29(3):617-625
24 P. K. Menon and V. R. Iragavarapu. Adaptive Techniques for Multiple Actuator Blending. AIAA-1998-4494
25邹晖,陈万春,王鹏,殷兴良.敏捷导弹气动力/侧向推力复合控制特性分析研究.北京航空航天大学学报. 2004, 30(3):192-196
26周锐,王军.导弹气动力/直接力自适应控制分配及优化设计.航空学报. 2007, 28(1):187-190
27 R. Hirokawa, K. Sato and S. Manabe. Autopilot Design for a Missile with Reaction-Jet Using Coefficient Diagram Method. AIAA-2001-4162
28李友年,贾晓洪.一种敏捷导弹控制系统的设计方法.航空兵器. 2005, 4:13-15
29贾晓洪,凡永华,杨军.一种气动力/直接力复合控制导弹自动驾驶仪设计.弹箭与制导学报. 2005, 25(3):1-3
30贾晓洪,凡永华,杨军.气动力/直接力复合控制导弹自动驾驶仪的鲁棒稳定性分析.弹箭与制导学报. 2005, 25(4):1-2
31王鹏,陈万春,殷兴良.空空导弹大角度姿态反作用喷气控制.航空学报. 2005, 26(3):263-267
32沈明辉,陈磊,吴瑞林,周伯昭.大气层内动能拦截弹的变增益鲁棒姿控系统设计研究.宇航学报. 2007, 28(3):562-565
33王宇航,马克茂.直接力与气动力复合控制系统姿态稳定问题研究.宇航学报. 2007, 28(4):840-844
34宋明军,魏明英,李君龙.某高制导精度拦截器稳定控制系统设计方法比较研究.现代防御技术. 2003, 31(3):37-40
35魏明英,宋明军.拦截器姿态控制系统切换控制方法研究.系统工程与电子技术. 2007, 29(1):118-120
36周荻,邵春涛.大气层内拦截弹直接侧向力/气动力混合控制系统设计.宇航学报. 2007, 28(5):1205-1209
37 H. K. Khalil. Nonlinear Systems. Third Edition. Publishing House of Electronics Industry, 2007:485-499
38 J. M. Biannic, P. Apkarian. Missile Autopilot Design via a Modified LPV Synthesis Technique. Aerospace Science and Technology. 1999, 3:153-160
39 W. J. Rugh, J. S. Shamma. Research on Gain Scheduling. Automatica. 2000, 36(10):1401-1425
40李中健,安锦文.全包线飞行控制系统设计方法研究.飞行力学. 2001, 19(1):5-8
41 R. W. Howard. Automatic Flight Controls in Fixed Wing Aircraft: The First 100 years. Aeronautical Journal. 77, 533-562
42 J. S. Shamma, J. R. Cloutier. Trajectory Scheduled Missile Autopilot Design. Proceedings of the 1st IEEE Conference on Control Applications, Dayton, OH. 1992:237-242
43 N. Sureshbabu, W. J. Rugh. Output Regulation with Derivative Information. IEEE Transactions on Automatic Control. 1995, 40(10):1755-1766
44 H. Tan, W. J. Rugh. Nonlinear Overtaking Optimal Control: Sufficiency, Stability and Approximation. IEEE Transactions on Automatic Control. 1998, 43(12):1703-1718
45 A. Leonessa, W. M. Haddad, V. Chellaboina. Nonlinear System Stabilization via Stability-based Switching. Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL. 1988:2983-2996
46 M. W. McConley, B. D. Appleby, M. A. Dahleh. Control Lyapunov Function Approach to Robust Stabilization of Nonlinear Systems. Proceedings of the American Control Conference, Albuquerque, NM. 1997:416-419
47 J. R. Cloutier, C. N. D’Souza, C. P. Mracek. Nonlinear Regulation and Nonlinear H-infinity Control via the State-dependent Riccati Equation Technique. Proceedings of the 1st International Conference on Nonlinear Problems in Aviation and Aerospace, Daytona, FL. 1996:117-130
48 T. S. Richardson, P. M. Davison, M. H. Lowenberg and M. di Bernardo. Control of Nonlinear Aircraft Models Using Dynamic State-Feedback Gain Scheduling. AIAA-2003-5503
49 C. D. C. Jones, M. H. Lowenberg and T. S. Richardson. Tailored Dynamic Gain-Scheduled Control. Journal of Guidance, Control and Dynamics. 2006, 29(6):1271-1281
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